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Презентация на тему Statistical Terminology

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Correlation
Statistical Terminology Correlation What is correlation?A statistical measurement that shows the relationship between two variables. Example: Height & Weight Pearson’s Correlation CoefficientPearson’s r, which measures a ‘normalized’ covariance (how changes in Correlation typesPositive correlationAn increase in one variable will lead to an increase Knowledge checkHeight and weightVehicle speed and travel timeGasoline prices and global oil Case StudyIn WWII, the US formed the Statistical Research Group to analyze Case Study (cont)When planes returned from missions, damage was unevenly distributed. The Case Study (cont)Tip: Set a variable to zero to test the probability.Ex.: Case StudyIn WWII, bombing accuracy had a high positive correlation with fighter Case StudyIn WWII, bombing accuracy had a high positive correlation with fighter Case StudyStatisticians often report that in assessing a child’s likeliness to succeed Case StudyStatisticians often report that in assessing a child’s likeliness to succeed Case Study	Economist recently announced that statistics prove the taller you are, the Case StudyEconomist recently announced that statistics prove the taller you are, the Statistical Terminology Essential TermsSampleA portion of a populationStratified SampleThe sample is chosen to reflect Essential TermsGeneralizationExtending conclusions from the sample to the population. Only possible is Essential TermsMeanThe average after adding and dividing all dataMedianThe middle number of Essential TermsDiscrete variableA variable with a finite amount of valuesContinuous variableA variable Variance“The average of the squared differences from the mean” ? how different Standard DeviationThe square root of the variance (more precise than variance) ? Standard Deviation ExampleDataset of height of cats in cm: [600, 470, 170, Standard Deviation ExampleIf the standard deviation is 147, then a datum is Sample Standard DeviationHow is the sample SD different from the population SD? Essential termsRegression Analysis: estimates relationships between X and Y variablesNull hypothesis: Assumes Descriptive & Inferential StatsDescriptive statisticsDescribes what’s happening in a datasetInferential statisticsGeneralizes sample findings to population Descriptive & Inferential Stats50% of all Russian men are named Ivan.20% of Question Design Open-ended vs. Closed-endedOpen-ended ? No response options providedClosed-ended ? A list of options provided Open-ended vs. Closed-endedOpen-ended used in pilot studies to determine most common optionsSubjective Closed-ended exampleForm a question asking about a student’s satisfaction with their high Question wordingBe aware of information and connotations in questions.“Do you favor or Question wordingBe aware of information and connotations in questions.“Do you favor or Question StructureAll reasonable responses included if closed.Responses shouldn’t overlap.One question at a Question StructureLeading questionsDo you think that the new cafeteria lunch menu offers Social desirability biasSensitive issues lead to misreportingUnderstated alcohol/drug use, tax evasionOverstated donations, Question OrderContrast effectsWhen order results in greater differences in responsesAssimilation effectsWhen responses Question Order Question Order Question Order The Good, The Bad, & The UglyHow likely would you be to The Good, The Bad, & The UglyWhat do you like to do Create your own surveySelect a dependent variable and at least two independent
Слайды презентации

Слайд 2 Correlation

Correlation

Слайд 3 What is correlation?
A statistical measurement that shows the

What is correlation?A statistical measurement that shows the relationship between two variables. Example: Height & Weight

relationship between two variables.
Example: Height & Weight


Слайд 4 Pearson’s Correlation Coefficient
Pearson’s r, which measures a ‘normalized’

Pearson’s Correlation CoefficientPearson’s r, which measures a ‘normalized’ covariance (how changes

covariance (how changes in one value are associated with

those of another), has a value between -1 and 1
1 – perfect positive linear correlation
0 – no linear correlation
-1 – perfect negative linear correlation


Слайд 5 Correlation types
Positive correlation
An increase in one variable will

Correlation typesPositive correlationAn increase in one variable will lead to an

lead to an increase in the other
Negative correlation
An increase

in one variable will lead to a decrease in the other
Note: In System Dynamics, these are called Positive and Negative Feedback loops

Слайд 6 Knowledge check
Height and weight
Vehicle speed and travel time
Gasoline

Knowledge checkHeight and weightVehicle speed and travel timeGasoline prices and global

prices and global oil production
Caloric intake and weight
Hours spent

watching TV and school grades
Car value and car mileage



Слайд 7 Case Study
In WWII, the US formed the Statistical

Case StudyIn WWII, the US formed the Statistical Research Group to

Research Group to analyze situations like the following:

You don’t

want your planes shot down by enemy fighters, so you armor them. Armor makes the plane heavier, and heavier planes are slower and use more fuel. Too much armor and too little armor is bad. Where do you armor them?

Слайд 8 Case Study (cont)
When planes returned from missions, damage

Case Study (cont)When planes returned from missions, damage was unevenly distributed.

was unevenly distributed. The fuselage and fuel system would

often have many bullet holes whereas the engines would have few. Should you put more armor on the fuselage?

Слайд 9 Case Study (cont)
Tip: Set a variable to zero

Case Study (cont)Tip: Set a variable to zero to test the

to test the probability.

Ex.: By imagining that a plane

is CERTAIN to be hit in the engine, the plane is CERTAIN to crash because planes can’t fly without working engines.

Either German planes happen to hit every part of a plane but the engine, or the engine is a point of total vulnerability.

Слайд 10 Case Study
In WWII, bombing accuracy had a high

Case StudyIn WWII, bombing accuracy had a high positive correlation with

positive correlation with fighter opposition. The more fighters, the

better the bombing accuracy. Why?

Слайд 11 Case Study
In WWII, bombing accuracy had a high

Case StudyIn WWII, bombing accuracy had a high positive correlation with

positive correlation with fighter opposition. The more fighters, the

better the bombing accuracy. Why?

Cloud cover. If there are too many clouds, fighters aren’t launched and bombers are inaccurate.

Слайд 12 Case Study
Statisticians often report that in assessing a

Case StudyStatisticians often report that in assessing a child’s likeliness to

child’s likeliness to succeed at school, those children whose

parents played classical music recordings for the unborn children will result in better grades. Why true?

Слайд 13 Case Study
Statisticians often report that in assessing a

Case StudyStatisticians often report that in assessing a child’s likeliness to

child’s likeliness to succeed at school, those children whose

parents played classical music recordings for the unborn children will result in better grades. Why true?

Adopting such a parental strategy indicates the parents are interested in the child’s intelligence.

Слайд 14 Case Study
Economist recently announced that statistics prove the

Case Study	Economist recently announced that statistics prove the taller you are,

taller you are, the more you are likely to

be paid. Why?

Слайд 15 Case Study
Economist recently announced that statistics prove the

Case StudyEconomist recently announced that statistics prove the taller you are,

taller you are, the more you are likely to

be paid. Why?

The lurking variable is more likely gender, as typically men are on average taller than women.

Слайд 16 Statistical Terminology

Statistical Terminology

Слайд 17 Essential Terms
Sample
A portion of a population
Stratified Sample
The sample

Essential TermsSampleA portion of a populationStratified SampleThe sample is chosen to

is chosen to reflect the population at large
Random Sample
The

sample is chosen by chance

Слайд 18 Essential Terms
Generalization
Extending conclusions from the sample to the

Essential TermsGeneralizationExtending conclusions from the sample to the population. Only possible

population. Only possible is sample is reflective.
Causation
When changes in

one variable affect the other
Elasticity
How much a change in one variable affects the other
Bias or Skew
Margin of Error



Слайд 19 Essential Terms
Mean
The average after adding and dividing all

Essential TermsMeanThe average after adding and dividing all dataMedianThe middle number

data
Median
The middle number of a dataset
Mode
Number(s) appearing most often

in a dataset

Слайд 20 Essential Terms
Discrete variable
A variable with a finite amount

Essential TermsDiscrete variableA variable with a finite amount of valuesContinuous variableA

of values
Continuous variable
A variable with many different values in

a range


Слайд 21 Variance
“The average of the squared differences from the

Variance“The average of the squared differences from the mean” ? how

mean” ? how different the data is

Ex.: [12, 12,

12, 12, 12]
Variance = 0
Ex.: [12, 12, 12, 12, 13]
Variance = 0.16
Ex.: [12, 12, 12, 12, 13013]
Variance = 27,044,160

Слайд 22 Standard Deviation
The square root of the variance (more

Standard DeviationThe square root of the variance (more precise than variance)

precise than variance) ? This is the main reason

for variance


Слайд 23 Standard Deviation Example
Dataset of height of cats in

Standard Deviation ExampleDataset of height of cats in cm: [600, 470,

cm:
[600, 470, 170, 430, 300]

Find the variance (Find

the mean, calculate the difference of each datum from the mean, square, then average).
21,704
Find the standard deviation (square root of the mean).
~147

Слайд 24 Standard Deviation Example
If the standard deviation is 147,

Standard Deviation ExampleIf the standard deviation is 147, then a datum

then a datum is “1 standard deviation from the

mean”. A datum “2 standard deviations is 296” and so on…

HOWEVER…

This is has been a ‘population’ standard deviation where each possible value was considered.

Слайд 25 Sample Standard Deviation
How is the sample SD different

Sample Standard DeviationHow is the sample SD different from the population

from the population SD? How to correct the calculation?

Divide

by ‘n-1’ instead of ‘n’ when finding both the variance and SD. Now find the sample SD and sample variance of the previous dataset.

Sample variance = 27,130
Sample SD = 164

Слайд 26 Essential terms
Regression Analysis: estimates relationships between X and

Essential termsRegression Analysis: estimates relationships between X and Y variablesNull hypothesis:

Y variables
Null hypothesis: Assumes no significant difference (states alternative

hypothesis false)
P-value: indicates strong evidence against null hypothesis (x <= 0.05), or weak evidence (x > 0.05) ? “Statistical significance”

Слайд 27 Descriptive & Inferential Stats
Descriptive statistics
Describes what’s happening in

Descriptive & Inferential StatsDescriptive statisticsDescribes what’s happening in a datasetInferential statisticsGeneralizes sample findings to population

a dataset
Inferential statistics
Generalizes sample findings to population


Слайд 28 Descriptive & Inferential Stats
50% of all Russian men

Descriptive & Inferential Stats50% of all Russian men are named Ivan.20%

are named Ivan.
20% of respondents are male
From 2000 to

2005, 70% of the land cleared in the Amazon and recorded in Brazilian government data was transformed into pasture.
Receive your college degree increases your lifetime earning by 50%.
Teachers named Joshua demonstrate inferior intellect to teachers named Timmy.

Слайд 29 Question Design

Question Design

Слайд 30 Open-ended vs. Closed-ended
Open-ended ? No response options provided
Closed-ended

Open-ended vs. Closed-endedOpen-ended ? No response options providedClosed-ended ? A list of options provided

? A list of options provided


Слайд 32 Open-ended vs. Closed-ended
Open-ended used in pilot studies to

Open-ended vs. Closed-endedOpen-ended used in pilot studies to determine most common

determine most common options
Subjective closed-ended ? Fewer options
Satisfaction with

economy
Fewer options avoids “recency effect”
Randomized order to ensure random bias
Objective closed-ended ? More options fine
Religious affliation


Слайд 33 Closed-ended example
Form a question asking about a student’s

Closed-ended exampleForm a question asking about a student’s satisfaction with their

satisfaction with their high school education (hint ? use

ordinal categories).
How can you mitigate the recency effect?

Слайд 34 Question wording
Be aware of information and connotations in

Question wordingBe aware of information and connotations in questions.“Do you favor

questions.

“Do you favor or oppose taking military action against

Saddam Hussein?”
Favor = 68%; Oppose = 25%


Слайд 35 Question wording
Be aware of information and connotations in

Question wordingBe aware of information and connotations in questions.“Do you favor

questions.

“Do you favor or oppose taking military action against

Saddam Hussein even if it meant that U.S. forces might suffer thousands of casualties?”
Favor = 43%; Oppose = 48%


Слайд 36 Question Structure
All reasonable responses included if closed.
Responses shouldn’t

Question StructureAll reasonable responses included if closed.Responses shouldn’t overlap.One question at

overlap.
One question at a time.
Bad: “How much confidence do

you have in Obama to handle domestic and foreign policy?”

Слайд 37 Question Structure
Leading questions
Do you think that the new

Question StructureLeading questionsDo you think that the new cafeteria lunch menu

cafeteria lunch menu offers a better variety of healthy

foods?

Neutral questions
How do you feel about the new cafeteria lunch menu compared to the old one?

Слайд 38 Social desirability bias
Sensitive issues lead to misreporting
Understated alcohol/drug

Social desirability biasSensitive issues lead to misreportingUnderstated alcohol/drug use, tax evasionOverstated

use, tax evasion
Overstated donations, church attendance
SDB higher when

interviewer is present
Include ‘Prefer Not to Answer’ option

Слайд 39 Question Order
Contrast effects
When order results in greater differences

Question OrderContrast effectsWhen order results in greater differences in responsesAssimilation effectsWhen

in responses
Assimilation effects
When responses are similar because of order


Слайд 40 Question Order

Question Order

Слайд 41 Question Order

Question Order

Слайд 42 Question Order

Question Order

Слайд 43 The Good, The Bad, & The Ugly
How likely

The Good, The Bad, & The UglyHow likely would you be

would you be to enroll in CookieDirect?
How organized and

interesting was the speaker?
How helpful do you think our customer service representatives are?
Should the government force you to pay higher taxes?
How would you rate the career of legendary writer Dovlatov?

Слайд 44 The Good, The Bad, & The Ugly
What do

The Good, The Bad, & The UglyWhat do you like to

you like to do for fun?
How dumb is President

Trump at making America great again?
Should teachers named Joshua offer pizza parties to obedient students?
In your opinion, how would you rate the quality of your work?
How do you feel about the following statement? We should reduce military spending.

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